THE MADISONIAN AND THE NATIONAL CONVENTION.—The Madisonian of Saturday, says: "We are becoming convinced that the probability is there will be no good result produced by the Convention. If one half of the delegates should be chosen by State Conventions and the rest by Districts, we have reason to apprehend a fatal rupture will occur in the General Convention, when angry discussions arise as to the manner of voting, &c. In such an event two or more Democratic candidates would be run—and that would be ruin. Our fears on this subject may be groundless, but when we say we entertain them we are in earnest. Matters have already gone to such an extremity that we do not believe either the District or the Machinery system will be adopted in all the States; and in the absence of unanimity in the mode of nominating the candidate, we have reason to anticipate great "confusion worse confounded." The Loco Foco leaders profess to go for principle—and yet they agree to support for President any one of a half a dozen candidates in the field, no one of whom entertains the same principles. Mr. Calhoun, Mr. Van Buren, Mr. Buchanan, Mr. Richard M. Johnson, and Mr. Cass. all on the Presidential course, have only one principle in common, that of desiring the honor of serving the public. Mr. Calhoun, with his great advocate, Mr. McDuffie, looks upon Slavery as "the corner stone of freedom," Mr. Buchanan, and possibly Mr. Van Buren, regard it as a stain and source of weakness; R. M. Johnson thinks it very convenient, and Mr. Cass has not yet sufficiently recovered from the attractions of the Court of the Tuileries and the fascinations of royalty, to have any opinion on so vulgar a subject. Mr. Calhoun is an ultra free trade man. Mr. Buchanan and Mr. R. M. Johnson, voted for the Tariff, Mr. Van Buren is on both sides, and Mr. Cass no where. In regard to a National Bank, all have been for it, and all, we believe, are now against it: and this is called principle!—New York American."